This post aims to explain Kant’s argument that things in themselves cannot be spatial in B66 (provided below, which we’ll call “P”). It will then evaluate the success of this argument against the neglected alternative view and, more specifically, the restriction view, which holds that all objects of outer sense must have the property of being spatial.
If there did not exist in you a power of a priori intuition; and if that subjective condition were not also at the same time, as regards its form, the universal a priori condition under which alone the object of this outer intuition is itself possible; if the object (the triangle) were something in itself, apart from any relation to you, the subject, how could you say that what necessarily exist in you as subjective conditions for the construction of a triangle, must of necessity belong to the triangle itself? You could not then add anything new (the figure) to your concepts (of three lines) as something which must necessarily be met with in the object, since this object is [on that view] given antecedently to your knowledge, and not by means of it. If, therefore, space (and the same is true of time) were not merely a form of your intuition, containing conditions a priori, under which alone things can be outer objects to you, and without which subjective conditions outer objects are in themselves nothing, you could not in regard to outer objects determine anything whatsoever in an a priori and synthetic manner.
P essentially boils down to a modus tollens argument. Kant establishes the conditional (C): if space were something more than “merely” a form of sensibility, then we could not have synthetic a priori knowledge (B66). He then relies on earlier arguments to make the claim that we do in fact have synthetic a priori knowledge. By modus tollens this entails that space cannot be more than a form of sensibility, and so it cannot be a feature of things in themselves.
Now we’ll break up the argument presented in P. Kant asks us to suppose two things. (A) That we do not have a “power” of a priori intuition, that is, suppose there is no a priori intuition we could use to produce universal and necessary facts (e.g. about geometry) before experience. And, (B) that space is “merely” a universal a priori condition under which alone the object of outer sense is itself possible (B66). With these two suppositions in mind, consider a triangle as a thing in itself – that is, as something apart from any relation it may bear to you (or any other subject). Kant asks, rhetorically, “how could you say that what necessarily exists in you as subjective conditions for the construction of a triangle, must of necessity belong to the triangle itself?” (B66). Because a priori intuition is the subjective condition for geometric construction, what we establish about triangles through a priori intuition are facts about triangles with respect to us (because a priori intuition is subjective). But to know a fact about an object in itself is to know something about that object independent of its relation to any subject (of experience). But it seems we can only know of objects insofar as they are related to us.
An elaboration. What can be established as synthetic a priori (e.g. about triangles) – necessary and universal propositions – only delimits the character of empirical reality. What is empirically real are appearances (of objects), not objects in themselves. In other words, our synthetic a priori knowledge of triangles is of how triangles must appear to us through our sense modalities. But if we consider a triangle apart from its relation to us, to sense, then we are considering the triangle over and above its “mere” appearance. Having necessary and universal knowledge of how triangles appear to you does not entail necessary universal knowledge about triangles in themselves. For the knowledge you can establish about triangles is only true insofar as the triangle is related to you. And what may be true of the appearance is not necessarily true of the object in itself. Consequently, in considering the triangle as a thing in itself, you cannot make necessary and universal claims about it, nothing about it can be established in a synthetic a priori way.
Kant elaborates somewhat. For you might think you can use your concept of three (non-parallel) lines to establish what “must necessarily be met with in the object” (B66), that is, considering a triangle in itself and your concept of three lines gives a necessary feature of other triangles (in themselves). But this is not so. For, (1) relations of concepts only yield analytic knowledge, so we must rely on an intuition. And, (2) if the triangle in itself is given to you (as an intuition) and you relate it to your concept of three-lines, then you establish that that triangle has three sides. But this does not establish any new knowledge because the three-lined-ness is already given to you along with the object. Your understanding has no work to do, for the concepts are already embodied in the “intuition” of the triangle in itself – there is no knowledge to “synthesize” in the relevant sense. So your knowledge of triangles-in-themselves cannot extend beyond your intuition of some triangle in itself. Even if you succeeded in discovering something “new”, this would only be a fact about the triangle you are considering, and not all triangles in themselves – that is, it would be an empirical rather than a priori fact. You cannot know that this object (e.g. this triangle) has that property (e.g. three-sided-ness) until you’ve encountered the object in experience. So if the object itself is given to you, rather than just the appearance, you cannot have synthetic a priori knowledge of that object (or its kind).
This partly addresses why we ostensibly can’t talk about things in themselves. When I have an intuition of (the appearance) of a triangle, I can say that that object, whatever else it may be, has the property such that it produces triangular representations in me. But can we say that the object in itself is triangular? No. Consider a world devoid of subjects to whom objects appear. If there are no particular appearances, then there are no particular properties you can apply to any object in itself. We cannot say that an object in itself has a particular property, because we don’t know what kinds of appearances it will produce. An object that I represent as a triangle is not triangular, rather it has the property of producing triangular representations in me – the latter does not entail the former. Without a subject to be affected, objects will not have properties, because the knowable properties of objects always trace back to their appearances in some mind.
So if we suppose (A) and (B), that is, that space is also a feature of things in themselves, then we cannot have synthetic a priori knowedge. This establishes (C). And because we know we have synthetic a priori knowledge (e.g. geometry), by modus tollens we must reject the antecedent of (C). Consequently, space can be nothing over and above one of our forms of sensibility.
For Kant’s argument in P to be effective, we need to have good reason to accept (C) and to accept that geometry is, in fact, synthetic a priori, provided that each step in P is valid. Do we?
You might think that we could still achieve synthetic a priori knowledge even if space was a feature of things in themselves. Suppose something like Newtonian space obtains of things in themselves, where space is an independently existing containter. You might think we could still obtain synthetic a priori knowledge. We could know that triangles have three sides by relating it to our concept of three lines (via some construction). Because all objects are in space, and my construction presumably occurs in space, what is true of my construction on that kind of thing will be true of others of that kind of thing insofar as they conform to certain spatial axioms. Because the Newtonian space is all-encompassing, whatever I construct in it should be equivalent to however I construct things in a priori intuition, because all possible objects of experience (that is, spatial objects), will be in this Newtonian space and determined by it – there are rules that objects universally and necessarily conform to. Because this process should be equivalent to construction in a priori intuition, the knowledge we obtain should be synthetic a priori in the same way. So, prima facie, it seems that considering space also as a feature of things in themselves does not threaten synthetic a priori knowledge. This would be reason to doubt (C).
On second glance, however, we see that any construction involving Newtonian space cannot be synthetic a priori. This is because any fact that I prove about how triangles are in Newtonian space is, in absence of a ceteris parabus clause, ineluctably a contingent fact. For if space is independent of my form of sensibility, then I cannot with “apodeictic certainty” know that space remains a certain way. For instance, I cannot know that space does not fluctuate between Euclidean and non-Euclidean manifestations. Nor can I know that it is Euclid’s axioms, in particular, that describe features of space, as opposed to some other set of similar but nonidentical axioms. So, I cannot know that some geometric fact I prove must be the case, for I cannot know that space remains constant; so whatever fact I prove may be subject to change – it is contingent on space’s being a certain way. So this knowledge is neither universal nor necessary and so cannot be a priori.
What would a ceteris parabus clause look like? It would be a stipulation that it is necessarily the case that space is a certain, constant way – Euclidean, say. If this is so, then we know that our constructions in Newtonian space are universal and necessary, and so a priori. Kant, however, will not allow this stipulation. We could not know that space, independently of us, is a certain way a priori. We have no grounds beyond experience for saying that space is necessarily this way rather than that, if we do not have a power of a priori cognition.
The important aspect of P is that a priori intuition (of space and time) constitutes necessary and invarient features of experience. If we are to have universal and necessary knowledge, it must trace back to a priori intuition, for there is no other universal and necessary feature of anything to which we could appeal in pursuit of synthetic a priori knowledge. This is why whatever can be known a priori cannot be a feature of a thing in itself, for if it were, then it would become empirical rather than a priori knowledge and lose its necessity. Suppose space were not a form of our sensibility. Then we would have no grounds whatsoever to assert that things in themselves are necessarily spatial or even just spatial. (It’s not even clear a subject could know what that would mean.)
P relies on accepting that geometry is synthetic a priori. But this, too, could be questioned. We saw that if space is also a feature of objects in themselves, that we do not have synthetic a priori knowledge. While Kant says that this shows space cannot be a feature of objects in themselves, someone else might think that instead we ought to reject geometry as being synthetic a priori. Maybe it is a contingent fact that space is such as it is, and that it has in fact remained constant. That would account for why geometric propositions seem universal and necessary, even if they are ultimately contingent and so not synthetic a priori. If this is so and Kant cannot establish the falsity of (C)’s consequent, then he has not successfully argued that space is nothing over and above the form of sensibility. To establish that geometry is synthetic a priori Kant needs to ground it in something constant, something universal and necessary. For Kant, this is the a priori intuition of space. But in P, Kant argues that because we have synthetic a priori knowledge, that space must be only a form of sensibility. We are grounding space as “merely” a form of sensibility in the fact that geometry is synthetic a priori. There is a sense in which each of these claims seems dependent on the other. If so, this could be problematic, but in the interests of space we’ll leave that to the commentators.
The restriction view is the thesis that for X to have the form of sensibility F, is just to say if X is to know an object through intuition, that object necessarily has the F property (e.g. spatiality). Kant’s argument in P shows that this is not so. Even if the object is known through intuition, so has the F property, we cannot know that the object is F as a matter of necessity, because this is empirical, and so contingent, knowledge. So P constitutes a successful reply to the restriction view.
It is less clear, however, whether the argument in P is a successful reply to the neglected alternative more generally. Namely the thesis that space, in addition to being a form of sensibility, is also a feature of things in themselves. Presumably, it is a contingent fact that humans have the form of sensibility that they do. And it is contingent that external space is the way that it is. But granting this, you might still think that there is a necessary connection between humans and the external space they are embedded in. We cannot say that objects are necessarily spatial, but rather that because they are contingently spatial, and we have space as a form of sensibility, there is a sort of necessary connection between humans and the world. Kant’s argument in P does not seem to rule out this possibility.